A man walks 5 km toward the south and then turns to his right. After walking 3 km, he turns to his left and walks another 5 km. In which direction is he now relative to his starting position?
Show Hint
Draw a quick rough sketch with small arrows. Visualizing the path directly on paper prevents confusion between left/right turns, especially when facing South.
Step 1: Understanding the Question:
This is a directional reasoning problem. We must map out the man's journey to find the direction of his final location relative to his starting point.
Step 2: Key Formula or Approach:
We can use a standard compass layout (North = Up, South = Down, East = Right, West = Left) or a Cartesian coordinate grid to track each movement step-by-step.
Step 3: Detailed Explanation:
Assume the starting point is the origin \(O (0, 0)\).
1. He walks 5 km South.
He arrives at point \(A\), facing South.
Coordinates of \(A = (0, -5)\).
2. He turns right.
A right turn from facing South directs him West.
He walks 3 km West to point \(B\).
Coordinates of \(B = (-3, -5)\).
3. He turns left.
A left turn from facing West directs him South.
He walks an additional 5 km South to his final destination, point \(C\).
Coordinates of \(C = (-3, -5 - 5) = (-3, -10)\).
Evaluating the final coordinates \((-3, -10)\) against the origin \((0, 0)\):
The negative x-value indicates a Westward displacement, and the negative y-value indicates a Southward displacement.
Consequently, his final position lies in the South-West direction from where he started.
